Blanket statements like these are never a good idea.
While many people have gotten along just fine without a page file, it is still recommended to have something available for legacy applications, and just for overall system stability, in case anything wants to use or expects the presence of such a file. In the end, a small amount of space taken up is inconsequential unless you are on really tiny SSD's.
"You['re] slowing down your system by making a swap file."
I don't see how this can possibly be true. Yes, I know what a page file is for, and as you yourself stated, it is for when the system runs out of RAM. How, then, does your system slow down if you don't actually run out of RAM? Furthermore, in the event that your system DOES run out of RAM, how would not having a pagefile help (BSOD) or having it on a traditional HDD make it faster (it won't.)? I already have my page file set to a static size to cover my needs.
You are also making large assumptions about my usage scenarios.
I process and edit large RAW files from my cameras in Lightroom and Photoshop on a regular basis, along with many other tasks. While I have made sure to have a good amount of RAM available (16GB) there may be cases where I may run out, especially if I am working on a RAW file with many layers. In extreme cases, one RAW with 7-8 layers can easily consume 6GB of RAM.
This comment is also vastly off topic for this discussion, as my recommendation was not to disable the page file, but to simply leave everything on the SSD, to take advantage of its speed. There's little point in getting an SSD, then not utilizing it.